42 relations: Basis function, Bézier curve, Box spline, Cauchy distribution, Chebyshev filter, Composite Bézier curve, Computer graphics, Computer-aided design, Computer-aided manufacturing, Continuous function, Curve fitting, De Boor's algorithm, Degree of a polynomial, Divided differences, Domain of a function, Exponential function, Fortran, Homogeneous coordinates, I-spline, Isaac Jacob Schoenberg, Least squares, Linear combination, Loss function, M-spline, Mathematics, Moving average, Normal distribution, Numerical analysis, Numerical differentiation, Overfitting, Penalty method, Piecewise, Polynomial, Savitzky–Golay filter, Smoothness, Spline (mathematics), Spline wavelet, Support (mathematics), T-spline, Tensor product, Terminology, Triangular function.
In mathematics, a basis function is an element of a particular basis for a function space.
A Bézier curve (pronounced in French) is a parametric curve frequently used in computer graphics and related fields.
In the mathematical fields of numerical analysis and approximation theory, box splines are piecewise polynomial functions of several variables.
The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.
Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters.
In geometric modelling and in computer graphics, a composite Bézier curve is a piecewise Bézier curve that is at least continuous.
Computer graphics are pictures and films created using computers.
Computer-aided design (CAD) is the use of computer systems to aid in the creation, modification, analysis, or optimization of a design.
Computer-aided manufacturing (CAM) is the use of software to control machine tools and related ones in the manufacturing of workpieces.
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
In the mathematical subfield of numerical analysis de Boor's algorithmC.
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions.
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.
Fortran (formerly FORTRAN, derived from Formula Translation) is a general-purpose, compiled imperative programming language that is especially suited to numeric computation and scientific computing.
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.
In the mathematical subfield of numerical analysis, an I-spline is a monotone spline function.
Isaac Jacob Schoenberg (April 21, 1903 – February 21, 1990) was a Romanian-American mathematician, known for his discovery of splines.
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.
In the mathematical subfield of numerical analysis, an M-spline is a non-negative spline function.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating series of averages of different subsets of the full data set.
In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.
In statistics, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit additional data or predict future observations reliably".
Penalty methods are a certain class of algorithms for solving constrained optimization problems.
In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain, a sub-domain.
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the signal-to-noise ratio without greatly distorting the signal.
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
In mathematics, a spline is a function defined piecewise by polynomials.
In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function.
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.
A T-spline surface can be thought of as a NURBS surface for which a row of control points is allowed to terminate without traversing the entire surface.
In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.
Terminology is the study of terms and their use.
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle.